Delayed Exponential Model Report

Stan Model

## S4 class stanmodel 'DE-modelSpec' coded as follows:
## data {
##   int<lower=0> N; // num observations
##   int<lower=0> ni; // num items
##   int<lower=0> ns; // num subjects
##   int<lower=0> nsi; // num subject-item combos
##   int<lower=0> si_lookup[ns, ni]; // lookup table for sparsely coded subject-item offsets
##   int<lower=0> nt; // num trials
##   int<lower=0> nc; // num strategies
##   real<lower=0> y[N]; // log RT 
##   int<lower=0> strategy[N]; // strategy for a given obs
##   int<lower=0> item[N]; // item for a given obs
##   int<lower=0> subject[N]; // subject for a given obs
##   int<lower=0> trial[N]; // trial for a given obs
## }
## 
## parameters {
##   real A; // = log_A, to be exponentialted later
##   real A_es[ns]; 
##   real A_ei[ni]; 
##   //real A_esi[ns,ni]; 
##   real A_esi[nsi];
##   real<lower=0> sigma_A_ei;
##   real<lower=0> sigma_A_es; 
##   real<lower=0> sigma_A_esi; 
## 
##   real B; // = log_B, to be exponentialted later
##   real B_es[ns]; 
##   real B_ei[ni]; 
##   //real B_esi[ns,ni]; 
##   real B_esi[nsi]; 
##   real<lower=0> sigma_B_ei; 
##   real<lower=0> sigma_B_es; 
##   real<lower=0> sigma_B_esi; 
## 
##   real T; 
##   real T_es[ns]; 
##   real T_ei[ni]; 
##   //real T_esi[ns,ni]; 
##   real T_esi[nsi];
##   real<lower=0> sigma_T_ei; 
##   real<lower=0> sigma_T_es; 
##   real<lower=0> sigma_T_esi; 
## 
##   real R; 
##   real R_es[ns]; 
##   real R_ei[ni]; 
##   //real R_esi[ns,ni]; 
##   real R_esi[nsi];
##   real<lower=0> sigma_R_ei; 
##   real<lower=0> sigma_R_es; 
##   real<lower=0> sigma_R_esi; 
## 
##   // add sigma variability 
## 
##   real<lower=0> sigma;
## }
## 
## transformed parameters {  
##   real y_hat[N];
##   real Alpha;
##   real Beta;// = B + B_es[subject[i]] + B_ei[item[i]] + B_esi[subject[i], item[i]];
##   real log_Rate;// = R + R_es[subject[i]] + R_ei[item[i]] + R_esi[subject[i], item[i]];
##   real log_Tau;// = T + T_es[subject[i]] + T_ei[item[i]] + T_esi[subject[i], item[i]];
## 
##   for(i in 1:N){ 
##     Alpha = exp(A + A_es[subject[i]] + A_ei[item[i]] + A_esi[si_lookup[subject[i], item[i]]]);
##     Beta = exp(B + B_es[subject[i]] + B_ei[item[i]] + B_esi[si_lookup[subject[i], item[i]]]);
##     log_Rate = R + R_es[subject[i]] + R_ei[item[i]] + R_esi[si_lookup[subject[i], item[i]]];
##     log_Tau = T + T_es[subject[i]] + T_ei[item[i]] + T_esi[si_lookup[subject[i], item[i]]];
##     // Tau = exp(Tau*Rate)-2; // old transformed version
##     // print(log_Alpha[i]);
##     // print(log_Beta[i]);
##     // print(Tau[i]);
##     // print(Rate[i]);
##     // print(exp(log_Alpha[i]) + exp(log_Beta[i]) * (Tau[i]+1) / (Tau[i] + trial[i]^Rate[i]));
##     // print(log(exp(log_Alpha[i]) + exp(log_Beta[i]) * (Tau[i]+1) / (Tau[i] + trial[i]^Rate[i])));
##     // print("");
##     y_hat[i] =  log(Alpha + Beta * (exp(log_Tau) + 1)/(exp(log_Tau) + exp(exp(log_Rate)*trial[i])));
##     // this resulted in no delayed start ever... : log(exp(log_Alpha) + (exp(log_Beta) * (exp(log_Tau) + 1) /(exp(log_Tau) + exp(log_Rate)*trial[i])));
##     // **old transformed version** log(exp(log_Alpha) + exp(log_Beta) * (Tau+1) / (Tau + trial[i]^Rate));
##     // go back to original version, but constrain Tau, Rate to be positive 
##   }
## }
## 
## model {
##   sigma ~ exponential(.1);
## 
##   A ~ normal(0, 6); // set as overall mean and sd of data
##   B ~ normal(8, 5); // set as mean, sd for retrieval trials
##   T ~ normal(5, 10); // was centered on 0
##   R ~ normal(-1, 2);
## 
##   sigma_A_es ~ exponential(1); 
##   sigma_A_ei ~ exponential(1);
##   sigma_A_esi ~ exponential(1);
## 
##   sigma_B_es ~ exponential(1);
##   sigma_B_ei ~ exponential(1);
##   sigma_B_esi ~ exponential(1);
## 
##   sigma_R_es ~ exponential(1);
##   sigma_R_ei ~ exponential(1);
##   sigma_R_esi ~ exponential(1);
## 
##   sigma_T_es ~ exponential(1);
##   sigma_T_ei ~ exponential(1);
##   sigma_T_esi ~ exponential(1);
##   
##   A_es ~ normal(0, sigma_A_es);
##   A_ei ~ normal(0, sigma_A_ei);
##   A_esi ~ normal(0, sigma_A_esi);
##   // for(i in 1:ns) {
##   //   for(j in 1:ni)
##   //     A_esi[i,j] ~ normal(0, sigma_A_esi);
##   // }
## 
##   B_es ~ normal(0, sigma_B_es);
##   B_ei ~ normal(0, sigma_B_ei);
##   B_esi ~ normal(0, sigma_B_esi);
##   // for(i in 1:ns) {
##   //   for(j in 1:ni)
##   //     B_esi[i,j] ~ normal(0, sigma_B_esi);
##   // }
## 
##   R_es ~ normal(0, sigma_R_es);
##   R_ei ~ normal(0, sigma_R_ei);
##   R_esi ~ normal(0, sigma_R_esi);
##   // for(i in 1:ns) {
##   //   for(j in 1:ni)
##   //     R_esi[i,j] ~ normal(0, sigma_R_esi);
##   // }
## 
##   T_es ~ normal(0, sigma_T_es);
##   T_ei ~ normal(0, sigma_T_ei);
##   T_esi ~ normal(0, sigma_T_esi);
##   // for(i in 1:ns) {
##   //   for(j in 1:ni)
##   //     T_esi[i,j] ~ normal(0, sigma_T_esi);
##   // }
## 
##   y ~ normal(y_hat, sigma); 
## }
## generated quantities {
##   vector[N] logLik; 
##   for(n in 1:N){
##     logLik[n] = normal_lpdf(y[n] | y_hat[n], sigma);
##   }
## }

Model Fit to Data

Diagnostics

Rhat distribution

Rhats for component parameters

Each spike represents the R-hat value for a particular component parameter. Below, very high values are examined more closely.

## [[1]]

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## [[2]]

## 
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## 
## [[5]]

Extreme Rhat values (Rhat > 1.1)

param mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat Parameter
A 7.1590135 0.0123961 0.0580937 7.0588567 7.1164544 7.1561451 7.2043385 7.2717960 21.962964 1.240784 Alpha
A_ei[1] -0.0559944 0.0068802 0.0451111 -0.1377226 -0.0872049 -0.0542590 -0.0265417 0.0486249 42.990409 1.103155 Alpha
A_ei[10] -0.0851730 0.0075675 0.0514284 -0.1781939 -0.1243041 -0.0859943 -0.0440694 0.0131603 46.184809 1.106629 Alpha
A_ei[2] 0.0295458 0.0079018 0.0513673 -0.0619943 -0.0046839 0.0292323 0.0617634 0.1385947 42.258912 1.107359 Alpha
A_es[1] -0.0602295 0.0264497 0.1022808 -0.2665103 -0.1273855 -0.0498706 0.0145676 0.1135085 14.953671 1.281300 Alpha
A_es[11] -0.0630869 0.0236899 0.0764952 -0.1939977 -0.1219553 -0.0640182 -0.0056018 0.0763137 10.426588 1.204158 Alpha
A_es[13] -0.0476521 0.0124725 0.0710838 -0.1826699 -0.1017960 -0.0531225 -0.0000477 0.0996358 32.481540 1.104618 Alpha
A_es[14] -0.1217076 0.0145787 0.0711481 -0.2568876 -0.1701622 -0.1205751 -0.0745273 0.0259815 23.816996 1.193546 Alpha
A_es[23] 0.4283653 0.0110122 0.0739961 0.2993459 0.3765877 0.4256696 0.4746997 0.5871269 45.150891 1.105070 Alpha
A_es[24] -0.4680687 0.0209216 0.0944300 -0.6458278 -0.5312233 -0.4711635 -0.3995773 -0.2941150 20.371825 1.208456 Alpha
A_es[26] 0.2029213 0.0123506 0.0752479 0.0318325 0.1566697 0.2007251 0.2493303 0.3439290 37.120461 1.130473 Alpha
A_es[28] -0.1821838 0.0155421 0.0902954 -0.3650655 -0.2359789 -0.1775651 -0.1257495 -0.0018523 33.752729 1.109866 Alpha
A_es[29] 0.1463884 0.0116261 0.0710509 0.0148794 0.0897996 0.1443273 0.1976718 0.2793910 37.348589 1.123136 Alpha
A_es[32] 0.3940432 0.0126646 0.0756080 0.2274275 0.3462428 0.3934361 0.4448858 0.5376414 35.641167 1.136440 Alpha
A_es[7] -0.5144022 0.0114312 0.0702630 -0.6542184 -0.5615990 -0.5049843 -0.4606921 -0.3930843 37.780440 1.150552 Alpha
A_esi[1] -0.3098821 0.0177267 0.0965457 -0.4979114 -0.3762055 -0.3077863 -0.2433833 -0.1161733 29.662665 1.116758 Alpha
A_esi[121] 0.0603930 0.0401718 0.1274447 -0.1506966 -0.0211078 0.0439617 0.1327246 0.3967366 10.064692 1.234377 Alpha
A_esi[122] -0.0295003 0.0385695 0.1101934 -0.2150282 -0.1074530 -0.0369701 0.0314135 0.2224485 8.162498 1.196428 Alpha
A_esi[199] 0.1715176 0.0524106 0.1186868 -0.0542766 0.0928074 0.1640801 0.2534088 0.4054980 5.128219 1.332831 Alpha
A_esi[213] 0.0531924 0.0806427 0.1561425 -0.1977511 -0.0628995 0.0126125 0.1922144 0.3493253 3.748969 1.695483 Alpha
A_esi[216] -0.0673011 0.0700699 0.1398130 -0.2993026 -0.1705888 -0.0819765 0.0266303 0.2122638 3.981361 1.480140 Alpha
A_esi[227] 0.2486996 0.0431081 0.1811748 -0.0722257 0.1056914 0.2558936 0.3943837 0.5852317 17.663576 1.143304 Alpha
A_esi[27] 0.0191716 0.0939987 0.1853268 -0.2753660 -0.1189742 -0.0167454 0.1355900 0.4413990 3.887164 1.502864 Alpha
A_esi[294] -0.2615720 0.0130514 0.0852461 -0.4180720 -0.3262175 -0.2622642 -0.2033099 -0.0917737 42.661394 1.148304 Alpha
A_esi[8] 0.0216870 0.0519142 0.1491944 -0.3015475 -0.0712529 0.0449947 0.1271823 0.2614537 8.259098 1.241665 Alpha
A_esi[90] 0.1712042 0.0395166 0.1232841 -0.0604201 0.0835743 0.1775546 0.2567076 0.4234880 9.733170 1.192764 Alpha
A_esi[92] 0.1102677 0.0197138 0.1173229 -0.1559973 0.0388053 0.1153311 0.1907423 0.3284819 35.417934 1.119665 Alpha
A_esi[97] -0.1123396 0.0228891 0.1025856 -0.3203695 -0.1769061 -0.1020546 -0.0383348 0.0635499 20.086953 1.172888 Alpha
B_es[1] -0.3029469 0.0152358 0.0902889 -0.4817609 -0.3584953 -0.3063341 -0.2407026 -0.1157037 35.118656 1.100191 Beta
B_es[15] -0.1497563 0.0247285 0.1128422 -0.3129475 -0.2255828 -0.1688262 -0.1027634 0.1381490 20.823203 1.126989 Beta
B_es[21] 0.0768801 0.0194205 0.0730546 -0.0531420 0.0286784 0.0719413 0.1224283 0.2264467 14.150559 1.169375 Beta
B_es[23] 0.0630333 0.0180568 0.0893035 -0.0935512 -0.0028992 0.0617090 0.1244881 0.2361559 24.459956 1.141181 Beta
B_es[24] 0.3099798 0.0273219 0.1203002 0.0850836 0.2117743 0.3340296 0.3947530 0.5228294 19.387009 1.173186 Beta
B_es[26] 0.1842207 0.0457216 0.1088438 -0.0115155 0.1054895 0.1783989 0.2537861 0.4038573 5.667141 1.339052 Beta
lp__ 5269.5982972 27.8653654 91.2795868 5098.7251666 5202.2963339 5265.3319949 5340.7091635 5431.6882987 10.730448 1.439611 Log Posterior
R 0.5771015 0.0521617 0.2155600 0.1314112 0.4149926 0.5649624 0.7578075 0.9884642 17.077861 1.238797 Rate
R_ei[5] -0.2384818 0.0189091 0.1053997 -0.4420277 -0.3008880 -0.2408723 -0.1759389 -0.0378522 31.069648 1.121042 Rate
R_ei[7] -0.0600719 0.0157497 0.1031553 -0.2887608 -0.1233653 -0.0613264 0.0088147 0.1427884 42.898275 1.102854 Rate
R_es[1] -1.6169760 0.0829917 0.3064217 -2.3024532 -1.7926731 -1.6119129 -1.3981007 -1.0202265 13.632311 1.247485 Rate
R_es[10] 0.2936123 0.0629387 0.2894436 -0.2460456 0.0883906 0.2839681 0.4987512 0.8811084 21.149106 1.122506 Rate
R_es[11] -0.9868877 0.0524694 0.3188931 -1.5848904 -1.1952153 -0.9827984 -0.7825418 -0.3723766 36.938452 1.113058 Rate
R_es[12] 1.1921918 0.0621608 0.3187886 0.6804215 0.9605262 1.1672558 1.3963693 1.8330321 26.300991 1.101806 Rate
R_es[14] 0.9129578 0.0585130 0.3512258 0.0995265 0.7160014 0.9125993 1.1856222 1.4783021 36.030383 1.140208 Rate
R_es[15] 0.3120032 0.2007870 0.6232842 -1.0286881 -0.0714279 0.4790993 0.7676059 1.1422289 9.636094 1.476822 Rate
R_es[16] 0.3348101 0.0964798 0.4255983 -0.5946830 0.0403552 0.3545554 0.6511435 1.0725567 19.459291 1.204100 Rate
R_es[17] -0.2714648 0.0612697 0.3494370 -0.9157469 -0.5231906 -0.2695276 -0.0178800 0.3871891 32.527155 1.126853 Rate
R_es[18] 0.7358820 0.1039509 0.3146499 -0.0356112 0.5552622 0.7469837 0.9679709 1.1792144 9.162181 1.236718 Rate
R_es[19] -0.0768486 0.0739568 0.3943659 -0.7694079 -0.3853886 -0.0811773 0.1959822 0.6253366 28.434320 1.113567 Rate
R_es[20] -0.3635596 0.1196556 0.6060302 -1.4060212 -0.9046062 -0.3110545 0.1288331 0.6324923 25.652083 1.171774 Rate
R_es[21] 0.8771027 0.0649394 0.2931633 0.3366187 0.7064394 0.8674804 1.0442071 1.5480934 20.379928 1.169328 Rate
R_es[22] 1.4275498 0.0541662 0.2859275 0.8394333 1.2111358 1.4490002 1.6503615 1.9100275 27.864786 1.137175 Rate
R_es[23] 0.9150397 0.0839889 0.3722016 0.1880112 0.6820455 0.9494698 1.1824522 1.5666653 19.638672 1.178766 Rate
R_es[24] -2.2467872 0.0891405 0.3335327 -2.8145815 -2.4629999 -2.2611072 -2.0528875 -1.5163432 13.999973 1.287294 Rate
R_es[25] -0.0239041 0.0831902 0.4240270 -0.7658607 -0.3564327 -0.0022999 0.3093856 0.7172386 25.980211 1.110951 Rate
R_es[26] -0.0920882 0.3676428 0.6756817 -1.3272807 -0.6395099 -0.1603096 0.5364200 1.0802069 3.377787 1.834716 Rate
R_es[3] 0.8087899 0.0929819 0.3159186 0.1579176 0.5828833 0.8096932 1.0516601 1.3540310 11.543927 1.277000 Rate
R_es[30] -0.5642590 0.1707682 0.5292769 -1.2797636 -0.9318016 -0.6725464 -0.4124879 0.6303718 9.606204 1.790263 Rate
R_es[31] 1.0385666 0.0589187 0.2730532 0.6340999 0.8128482 1.0315107 1.1953542 1.7126804 21.477702 1.166735 Rate
R_es[32] 0.2777120 0.1062563 0.5580897 -0.6268639 -0.1070437 0.2192322 0.5894673 1.4629785 27.586634 1.153826 Rate
R_es[4] -0.5852800 0.0942715 0.4455881 -1.2594969 -0.9028636 -0.6277550 -0.3028619 0.3793143 22.341178 1.232477 Rate
R_es[6] -0.2128286 0.0712792 0.3926866 -0.8055120 -0.5208267 -0.2632692 0.0208088 0.6709788 30.350547 1.172733 Rate
R_esi[11] 0.1818529 0.0238935 0.1630826 -0.1243546 0.0549306 0.1780541 0.3160222 0.4592323 46.585943 1.103697 Rate
R_esi[12] 0.4412543 0.0424070 0.1881404 0.1092952 0.3215382 0.4139991 0.5537892 0.8120561 19.682928 1.298687 Rate
R_esi[121] -0.1914270 0.0639411 0.1949776 -0.4910365 -0.3370637 -0.2072970 -0.0861493 0.2459675 9.298416 1.261747 Rate
R_esi[122] 0.1184200 0.1984516 0.3284272 -0.2904446 -0.1270730 0.0223625 0.2224394 0.8228514 2.738856 2.061709 Rate
R_esi[124] 0.1939386 0.0491687 0.2886601 -0.3294979 -0.0350402 0.2255040 0.4155782 0.7002951 34.466440 1.107720 Rate
R_esi[13] -0.1785632 0.0325214 0.1849919 -0.4875726 -0.3099509 -0.1870618 -0.0408584 0.1974521 32.356821 1.204108 Rate
R_esi[14] -0.1177332 0.0290556 0.1934759 -0.4942493 -0.2533382 -0.1330945 0.0303155 0.2044963 44.339776 1.110815 Rate
R_esi[141] -0.1291114 0.0559515 0.2672307 -0.8184303 -0.2569544 -0.0807004 0.0626077 0.2461514 22.811291 1.156231 Rate
R_esi[147] 0.1889102 0.0480009 0.2229079 -0.2812926 0.0757488 0.2070072 0.3240937 0.5700435 21.565097 1.191789 Rate
R_esi[15] 0.1089445 0.0267649 0.1643365 -0.2093468 -0.0189123 0.1262324 0.2320900 0.3930467 37.699746 1.117241 Rate
R_esi[162] -0.0816235 0.0503972 0.2250428 -0.5064320 -0.2433850 -0.0836270 0.0879566 0.3208507 19.939657 1.140186 Rate
R_esi[17] -0.0944173 0.0305342 0.1814943 -0.4410316 -0.2263688 -0.0785376 0.0536378 0.1945448 35.330844 1.148046 Rate
R_esi[171] -0.3282420 0.0286149 0.1712679 -0.6687544 -0.4228409 -0.3217537 -0.2464904 0.0674322 35.823508 1.124655 Rate
R_esi[18] 0.2269805 0.0256906 0.1483995 -0.0459485 0.1038219 0.2346381 0.3363978 0.4918780 33.367036 1.115600 Rate
R_esi[196] 0.2853967 0.0426969 0.1826553 -0.0655702 0.1471482 0.3018306 0.4173456 0.6243029 18.300870 1.203717 Rate
R_esi[199] -0.0000530 0.1143433 0.2096996 -0.3178103 -0.1560615 -0.0219783 0.1265038 0.4651528 3.363366 1.674161 Rate
R_esi[20] -0.2107420 0.0266380 0.1736038 -0.5340272 -0.3376072 -0.2051693 -0.0946386 0.0966683 42.473281 1.136908 Rate
R_esi[213] -0.2671692 0.1911765 0.3471565 -0.6942953 -0.5385876 -0.3919725 0.0089403 0.4606610 3.297477 1.882712 Rate
R_esi[216] -0.3358729 0.1104890 0.2281111 -0.7154303 -0.5062788 -0.3492138 -0.1802320 0.1506606 4.262403 1.493395 Rate
R_esi[22] 0.7647588 0.0280233 0.1593151 0.4543011 0.6533287 0.7534896 0.8776001 1.0846654 32.320302 1.138095 Rate
R_esi[220] 0.4053457 0.0318280 0.2343522 -0.0484771 0.2627223 0.3873670 0.5700418 0.9039638 54.215051 1.111965 Rate
R_esi[226] -0.3527553 0.0512847 0.2603834 -1.0504512 -0.4953260 -0.3089548 -0.1767859 0.0673127 25.778073 1.107686 Rate
R_esi[227] -0.2385199 0.1179339 0.3967215 -0.8400584 -0.5553403 -0.3200822 0.0852521 0.5097580 11.316024 1.202158 Rate
R_esi[228] 0.5075990 0.0642549 0.2711100 -0.1145225 0.3490900 0.5325221 0.6910760 0.9700270 17.802421 1.150218 Rate
R_esi[235] -0.1125901 0.1047553 0.2680047 -0.5438952 -0.2932461 -0.1413737 0.0566754 0.4840844 6.545357 1.323837 Rate
R_esi[236] 0.3921971 0.0408807 0.2369553 -0.1706549 0.2525416 0.4206613 0.5452448 0.7954855 33.596683 1.103053 Rate
R_esi[238] -0.2509864 0.0362018 0.2281821 -0.6790989 -0.4031506 -0.2500144 -0.1041485 0.1740998 39.728597 1.126648 Rate
R_esi[240] 0.0967569 0.1053311 0.3056829 -0.6465952 -0.0098151 0.1508686 0.2970877 0.5868170 8.422268 1.264753 Rate
R_esi[241] 0.2711724 0.0737730 0.3146298 -0.4615952 0.1117162 0.3230229 0.4641191 0.7751021 18.188855 1.229206 Rate
R_esi[242] 0.2538862 0.0580602 0.2684532 -0.3089076 0.1314394 0.2762016 0.4344276 0.6919438 21.378649 1.135178 Rate
R_esi[248] 0.1620792 0.0266619 0.1746064 -0.1279257 0.0358718 0.1588772 0.2838257 0.4832164 42.888313 1.110779 Rate
R_esi[27] -0.4174937 0.0850486 0.2013592 -0.8030523 -0.5630134 -0.4306356 -0.2900791 -0.0390789 5.605428 1.373212 Rate
R_esi[272] 0.1246892 0.0340772 0.2037526 -0.2738641 -0.0108215 0.1230579 0.2678903 0.5550119 35.750297 1.114929 Rate
R_esi[276] -0.1502989 0.0300012 0.2086030 -0.5840874 -0.2746974 -0.1517844 -0.0013218 0.2449351 48.346291 1.106644 Rate
R_esi[279] 0.2356271 0.0582786 0.2802923 -0.3493935 0.0548746 0.2637187 0.4390233 0.7208132 23.131542 1.162378 Rate
R_esi[284] -0.4351494 0.0237468 0.1584120 -0.7148030 -0.5618869 -0.4242090 -0.3369905 -0.1444215 44.500762 1.116261 Rate
R_esi[285] -0.2865960 0.0250123 0.1560522 -0.5742976 -0.4080510 -0.2782387 -0.1743600 -0.0118224 38.925356 1.106139 Rate
R_esi[287] 0.1081820 0.0219885 0.1524560 -0.1687612 0.0076157 0.1191031 0.2127611 0.3680784 48.072459 1.116735 Rate
R_esi[289] 0.0994398 0.0269992 0.1508175 -0.1999101 -0.0139449 0.1043236 0.1981939 0.3910408 31.203302 1.109348 Rate
R_esi[290] 0.4478294 0.0304589 0.1437686 0.1662208 0.3452105 0.4495111 0.5415145 0.7205627 22.279212 1.115552 Rate
R_esi[292] 0.7459793 0.0290744 0.1699443 0.4407513 0.6212923 0.7305057 0.8621174 1.0903895 34.165824 1.111960 Rate
R_esi[298] -0.1879111 0.0614638 0.3316716 -0.8475150 -0.4077229 -0.1745067 0.0456762 0.4064282 29.119095 1.169147 Rate
R_esi[31] -0.1155675 0.0467426 0.2756257 -0.7013542 -0.3054513 -0.0819628 0.0913146 0.3465647 34.770690 1.147269 Rate
R_esi[32] -0.2521753 0.0378706 0.2548411 -0.7509378 -0.4379926 -0.2466031 -0.0820319 0.2371724 45.282988 1.129861 Rate
R_esi[33] 0.1355846 0.0703379 0.4301401 -0.5281795 -0.2052266 0.0944748 0.4228168 1.0000378 37.397367 1.148809 Rate
R_esi[35] -0.4871896 0.0797797 0.4124282 -1.1583632 -0.7779008 -0.5602966 -0.2783535 0.4197089 26.724616 1.144851 Rate
R_esi[49] -0.0378618 0.0324239 0.2169760 -0.4163585 -0.2057504 -0.0369977 0.1102995 0.4167276 44.780903 1.133388 Rate
R_esi[72] -0.1016334 0.0395333 0.2401089 -0.5201799 -0.2893596 -0.1035939 0.0735813 0.3783057 36.888473 1.117542 Rate
R_esi[8] 0.1146268 0.2528064 0.6264274 -0.9492816 -0.3559337 0.0403949 0.6550688 1.2462402 6.139960 1.410179 Rate
R_esi[88] -0.3255000 0.0243805 0.1596703 -0.5951848 -0.4261705 -0.3343458 -0.2428701 0.1094496 42.890617 1.115388 Rate
R_esi[90] -0.1823934 0.0380185 0.1844707 -0.5351464 -0.3348132 -0.1705024 -0.0397152 0.1419367 23.543115 1.136427 Rate
R_esi[92] 0.1257735 0.0443971 0.1451180 -0.1485953 0.0305726 0.1232145 0.2254300 0.4275953 10.683966 1.203462 Rate
R_esi[95] 0.2512792 0.0282801 0.1556182 -0.0327653 0.1460086 0.2506800 0.3501580 0.5630976 30.280259 1.149969 Rate
sigma_B_esi 0.0316019 0.0024852 0.0085183 0.0190329 0.0247189 0.0309673 0.0374743 0.0493529 11.748808 1.417519 Sigma
sigma_R_es 0.9698941 0.0151197 0.1258148 0.7459812 0.8772076 0.9570315 1.0520036 1.2254195 69.243561 1.100595 Sigma
sigma_T_es 15.8302167 0.5292513 2.1585565 12.0629221 14.3602431 15.5624204 17.2499968 20.5437154 16.634240 1.248595 Sigma
sigma_T_esi 2.5521649 0.1199035 0.3796703 1.9102731 2.2758837 2.5083077 2.8270337 3.3287811 10.026506 1.300553 Sigma
T 24.8376773 1.8722723 3.9096730 18.2091365 21.0931164 24.9041843 27.7857284 32.2205663 4.360566 2.085644 Tau
T_es[1] -21.3036140 1.9880156 4.1516096 -29.0049390 -24.5183006 -21.5959939 -17.4430592 -14.6403267 4.361073 1.887950 Tau
T_es[11] -21.5773460 1.9387600 4.4229099 -29.9810531 -25.2560239 -21.3639846 -17.9957129 -14.5473926 5.204369 1.856211 Tau
T_es[12] -1.1151960 1.9488052 5.7457293 -12.5245988 -4.6482744 -1.3186781 1.8538118 12.0586107 8.692675 1.274132 Tau
T_es[13] 19.7798528 1.9946289 10.0875807 2.1274197 13.5139555 19.5269003 25.0017579 42.5866913 25.577015 1.130543 Tau
T_es[14] 15.0829214 2.7300007 11.6265823 -7.0808443 7.6087248 14.7300814 21.6811391 40.5120971 18.137550 1.245992 Tau
T_es[15] 1.2720593 4.2065508 13.4058487 -19.8440594 -13.2463554 4.6732808 10.5206343 25.9761414 10.156319 1.509262 Tau
T_es[16] 12.4924787 3.1225321 13.7294663 -7.4032909 1.7985309 10.0442288 21.2441971 42.9932132 19.332743 1.265775 Tau
T_es[17] -1.7898363 1.7560305 8.0626013 -14.0426824 -7.0418222 -2.1437625 1.2062108 18.5358424 21.080759 1.238460 Tau
T_es[18] 21.6823887 3.9063763 12.3256254 -4.6830571 14.4339905 21.5433226 28.8797305 48.7207282 9.955653 1.246128 Tau
T_es[19] 8.0550452 1.9680348 10.7114489 -8.3674373 -0.0441145 7.1773844 14.8990538 33.9824505 29.623126 1.130780 Tau
T_es[20] -9.8752962 3.3599738 9.7955925 -24.7789785 -16.7873678 -11.9917573 -3.1038382 11.1420296 8.499427 1.441426 Tau
T_es[21] 24.7868057 2.9919789 10.7335513 5.6237086 16.3179266 25.1303631 32.2743205 44.5206547 12.869742 1.493265 Tau
T_es[22] 14.4319332 2.1800223 9.4954655 -2.6184386 6.7072243 13.7415205 21.6172339 33.5302961 18.971893 1.250258 Tau
T_es[23] 17.9933022 2.9601371 11.5998493 -2.3989305 11.4894096 17.1231363 25.0246198 40.3393550 15.356104 1.255974 Tau
T_es[24] -29.1283898 2.5812551 6.9434950 -42.0965577 -35.4028981 -27.4282463 -23.4754595 -19.1708516 7.235931 1.519888 Tau
T_es[25] 9.2828125 2.3042464 9.3387326 -4.8379358 2.4989503 7.6472432 14.4712804 30.2298271 16.425480 1.187196 Tau
T_es[26] -9.1178971 6.7410375 12.0466774 -25.9008104 -19.8625987 -10.7914144 1.1075942 12.5322539 3.193604 2.159063 Tau
T_es[27] 22.6492012 1.7331640 9.5223676 6.8848338 15.8493374 21.3114172 29.3090841 42.6731593 30.186348 1.139684 Tau
T_es[28] -20.2997868 1.6531427 3.7597585 -27.3034967 -22.9303107 -21.0058800 -17.0751219 -13.7514365 5.172485 1.721024 Tau
T_es[3] 24.8362698 3.1501938 10.7864988 5.2892922 16.1061299 25.1052790 33.0086806 43.8049864 11.724287 1.208034 Tau
T_es[30] -10.8779710 4.3437085 11.8507511 -23.7580808 -17.8964234 -14.3214139 -9.9074881 22.5273812 7.443384 2.202752 Tau
T_es[32] -12.9102986 2.5271456 9.7103814 -25.2217402 -19.3151053 -15.8504685 -8.9264751 13.8511063 14.764273 1.328253 Tau
T_es[4] -18.2593738 1.5855788 4.9088328 -26.6689673 -21.9726528 -18.6595325 -14.8072359 -7.5989682 9.584751 1.755544 Tau
T_es[5] -16.1161550 1.5278893 6.5907144 -24.4313111 -20.0034842 -16.9673686 -14.2143022 1.9913278 18.607209 1.186731 Tau
T_es[6] -11.2903922 1.0731185 6.3307983 -20.5555738 -15.8604993 -11.7404957 -8.7492549 4.5456421 34.803396 1.139182 Tau
T_es[7] -17.7792019 1.4587213 4.1080511 -25.5732838 -20.9864893 -17.0261605 -14.7191159 -11.0431576 7.930983 1.483200 Tau
T_es[8] -12.3195041 1.5283619 5.0582789 -20.7147181 -16.5311014 -12.3033772 -8.5220066 -2.4298827 10.953505 1.483048 Tau
T_es[9] -18.2862047 1.8158872 4.3063810 -26.6589366 -21.5347154 -18.2332437 -14.8779769 -11.0472221 5.624024 1.593656 Tau
T_esi[101] 1.1980161 0.2542888 1.6088764 -1.6805851 0.0427192 1.1881937 2.1589826 4.2959723 40.030494 1.125063 Tau
T_esi[110] -0.7924516 0.5043011 2.5661027 -6.6883843 -2.5661724 -0.5929840 0.9375339 3.8520825 25.892153 1.247972 Tau
T_esi[112] 0.8543186 0.5957476 2.7805899 -3.9582469 -1.0863843 0.8091894 2.5257504 6.8033136 21.784584 1.132424 Tau
T_esi[116] -2.1277303 0.4380469 2.7596990 -7.9039005 -3.5784744 -1.9239082 -0.3479921 3.0894329 39.690103 1.137779 Tau
T_esi[12] 0.2269953 0.3294608 2.3218160 -4.2836560 -1.3158954 0.1019329 1.7769935 4.7788439 49.664741 1.116854 Tau
T_esi[122] 0.4052332 0.6013506 2.8673174 -6.3621906 -1.2500690 0.4974285 2.2648758 5.5404731 22.735060 1.215921 Tau
T_esi[130] 0.8288830 0.6408323 2.7809569 -4.7801314 -0.9661687 0.7036042 2.7731488 6.0653580 18.832142 1.244795 Tau
T_esi[134] 1.0286967 0.3561069 2.5940541 -3.8528444 -0.8635178 1.0511332 2.7063902 6.6962193 53.063684 1.122098 Tau
T_esi[140] 0.1819118 0.6211022 2.5623261 -5.1147571 -1.4771979 0.2784313 1.8078431 5.1025541 17.019338 1.201856 Tau
T_esi[143] -1.7107902 0.5775811 3.2534653 -8.4298265 -3.7734862 -1.4597846 0.3431474 4.4232104 31.729726 1.163776 Tau
T_esi[144] 0.7253008 0.5511457 2.4918907 -4.0698829 -0.8065971 0.5924152 2.7333266 5.1676054 20.442086 1.154786 Tau
T_esi[153] 0.3228297 0.3837436 2.3295313 -4.4433765 -1.1531749 0.1960099 2.1949142 4.5599757 36.851460 1.131863 Tau
T_esi[162] -1.6899839 0.7694299 3.1859254 -7.3662228 -3.8224258 -1.9719393 0.7499709 4.9913363 17.144826 1.166023 Tau
T_esi[181] 0.5128109 0.5618887 2.5552932 -4.7675614 -1.1018553 0.5713892 2.1317981 5.2254015 20.681442 1.124706 Tau
T_esi[187] 0.8303066 0.3301464 2.0638311 -2.8890254 -0.7253205 0.7328131 2.3278480 4.8763454 39.078265 1.123350 Tau
T_esi[196] -0.5702764 0.3972428 2.7548063 -6.0306890 -2.3466911 -0.6942806 1.1123539 5.4032915 48.091702 1.131955 Tau
T_esi[202] 0.2432132 0.3591571 2.5949050 -4.7924263 -1.6482516 0.3932843 2.0002067 4.9305844 52.200426 1.127308 Tau
T_esi[211] -0.5116910 0.4066318 2.5346928 -5.0105056 -2.2128218 -0.7559506 1.1447958 4.9622564 38.855091 1.127153 Tau
T_esi[212] 0.1522740 0.4314700 2.5595998 -5.1041411 -1.3982068 0.1208744 1.8017383 4.8757380 35.191922 1.131383 Tau
T_esi[221] -0.1938625 0.4768863 2.4572765 -4.5023534 -1.8766639 -0.4983891 1.7088189 4.8404728 26.550848 1.207872 Tau
T_esi[224] -1.1500105 0.7209549 2.5115038 -5.3834281 -2.6990777 -1.2896804 0.2142229 4.8736229 12.135328 1.179674 Tau
T_esi[227] 1.3424166 0.6561452 2.7250793 -4.2969868 -0.3273276 1.8051141 3.4060316 5.5627070 17.248778 1.253454 Tau
T_esi[228] -1.4487201 0.7229746 2.5252273 -6.6209948 -3.1345094 -1.5767446 0.3743817 3.4532868 12.199861 1.184844 Tau
T_esi[235] 2.1657943 0.4637763 2.5404421 -3.4275786 0.3889326 2.1898329 4.0865298 6.4963707 30.005547 1.119584 Tau
T_esi[240] -0.4108664 0.8033435 2.3846397 -4.0082686 -2.1705437 -0.7698543 1.0781355 4.4492429 8.811360 1.210838 Tau
T_esi[241] -1.0599827 0.7772377 2.4272731 -5.4564071 -2.9251230 -1.1056537 0.9376360 3.1419109 9.752804 1.244834 Tau
T_esi[256] -0.5379946 0.2637348 1.5632209 -3.3537027 -1.5732930 -0.7440457 0.5079150 2.7792659 35.132235 1.122040 Tau
T_esi[278] -1.2300208 0.3192960 2.1723501 -5.2147445 -2.6999886 -1.3323981 0.3376956 3.5599414 46.288460 1.124715 Tau
T_esi[279] -1.1169861 0.4575561 2.1767702 -4.5253141 -2.5375535 -1.4600798 0.0197746 4.4480664 22.632709 1.136844 Tau
T_esi[33] -3.9457607 0.2826191 1.9784936 -8.1442935 -5.1803106 -3.8654963 -2.6589062 -0.1867644 49.007920 1.130855 Tau
T_esi[35] -2.5322768 0.3668222 2.1384988 -6.5011906 -3.8240879 -2.7543204 -1.6844485 2.7585571 33.986529 1.100761 Tau
T_esi[42] 0.3062900 0.3586808 2.2565473 -3.9648985 -1.0899764 0.0800600 1.7011864 5.8355302 39.579710 1.117692 Tau
T_esi[58] 0.4256077 0.2660988 1.9179751 -2.9389609 -1.1533705 0.4052233 1.8256867 3.9595110 51.951757 1.111541 Tau
T_esi[76] 0.6942880 0.3920715 2.5635651 -3.6759024 -1.0464106 0.5134721 2.4020215 5.9755826 42.752178 1.115181 Tau
T_esi[8] -2.8640991 0.8419444 2.6691710 -7.5690863 -4.9336450 -3.0198488 -0.9722765 2.3957821 10.050460 1.208972 Tau
T_esi[94] -0.0627672 0.3923775 2.5576629 -5.2655557 -1.6696166 -0.0597038 1.7587461 4.4674629 42.489192 1.123695 Tau
log_Tau 12.7303764 1.4829917 8.2775208 3.9703000 7.2537946 10.0551800 14.9831107 36.5305905 31.154668 1.117914 Transformed

Subject-level Rhats

Item-level Rhats

Interaction Rhats (white = missing interaction level)